A351970 a(0) = 1; a(n) = Sum_{k=0..floor(n/3)} binomial(n,3*k) * a(k).

1, 1, 1, 2, 5, 11, 22, 43, 85, 171, 351, 738, 1590, 3498, 7827, 17757, 40725, 94113, 218439, 507852, 1180395, 2739312, 6342084, 14642100, 33703182, 77344686, 176984406, 403901722, 919533655, 2089000936, 4737194867, 10726221713, 24257223605, 54805216567

Offset: 0

Author

Ilya Gutkovskiy, Feb 26 2022

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A027826, A351971.

Programs

Mathematica

a[0] = 1; a[n_] := a[n] = Sum[Binomial[n, 3 k] a[k], {k, 0, Floor[n/3]}]; Table[a[n], {n, 0, 33}]
nmax = 33; A[] = 1; Do[A[x] = A[x^3/(1 - x)^3]/(1 - x) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]

Formula

G.f. A(x) satisfies: A(x) = A(x^3/(1 - x)^3) / (1 - x).

E.g.f.: exp(x) * Sum_{n>=0} a(n) * x^(3*n) / (3*n)!.